Z→bb¯and chiral currents in Higgsless models

Abstract

In this paper we compute the flavor-dependent chiral-logarithmic corrections to the decay $Z\ensuremath{\rightarrow}b\overline{b}$ in the three-site Higgsless model. We compute these corrections diagrammatically in the gaugeless limit in which the electroweak couplings vanish. We also compute the chiral-logarithmic corrections to the decay $Z\ensuremath{\rightarrow}b\overline{b}$ using a renormalization group equation analysis in effective field theory, and show that the results agree. In the process of this computation, we compute the form of the chiral current in the gaugeless limit of the three-site model, and consider the generalization to the $N$-site case. We elucidate the Ward-Takahashi identities which underlie the gaugeless limit calculation in the three-site model, and describe how the result for the $Z\ensuremath{\rightarrow}b\overline{b}$ amplitude is obtained in unitary gauge in the full theory. We find that the phenomenological constraints on the three-site Higgsless model arising from measurements of $Z\ensuremath{\rightarrow}b\overline{b}$ are relatively mild, requiring only that the heavy Dirac fermion be heavier than 1 TeV or so, and are satisfied automatically in the range of parameters allowed by other precision electroweak data.